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Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data

Author

Listed:
  • Mike Danilov
  • Víctor J. Yohai
  • Ruben H. Zamar

Abstract

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S -estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the definition of S -estimators of multivariate location and scatter to simultaneously deal with missing data and outliers. We show that the proposed estimators are strongly consistent under elliptical models when data are missing completely at random . We derive an algorithm similar to the Expectation-Maximization algorithm for computing the proposed estimators. This algorithm is initialized by an extension for missing data of the minimum volume ellipsoid. We assess the performance of our proposal by Monte Carlo simulation and give some real data examples. This article has supplementary material online.

Suggested Citation

  • Mike Danilov & Víctor J. Yohai & Ruben H. Zamar, 2012. "Robust Estimation of Multivariate Location and Scatter in the Presence of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1178-1186, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1178-1186
    DOI: 10.1080/01621459.2012.699792
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.699792
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    Citations

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    Cited by:

    1. Stefan Van Aelst, 2015. "Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 478-481, September.
    2. Leung, Andy & Yohai, Victor & Zamar, Ruben, 2017. "Multivariate location and scatter matrix estimation under cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 59-76.
    3. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 441-461, September.
    4. Christophe Croux & Viktoria Öllerer, 2015. "Comments on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 462-466, September.
    5. Leung, Andy & Zhang, Hongyang & Zamar, Ruben, 2016. "Robust regression estimation and inference in the presence of cellwise and casewise contamination," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 1-11.
    6. Claudio Agostinelli & Andy Leung & Victor Yohai & Ruben Zamar, 2015. "Rejoinder on: Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 484-488, September.

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